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ECON 337 Assignment 1 Fall 2007

# ECON 337 Assignment 1 Fall 2007 - manipulations but make...

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ECON 337 Assignment 1 Fall 2007 Consider the following data set: x1 x2 x3 y 2 28 23 123 5 23 45 150 5 27 12 164 7 18 54 205 10 11 37 214 1 If y is regressed on x1, find the following using the matrix method. Feel free to use EXCEL to help with the matrix manipulations, but make sure you understand what is going on. Check your work if you wish using MINITAB or other statistics software. a) 1 ) ( - X X t . b) ) ( X X adj t . c) The hat matrix. d) bx a y + = ˆ d) The OLS line equation if the graph is forced through the origin. 2. If y is regressed on x1, x2, and x3 (i.e. multiple regression), find the following using the matrix method. Feel free to use EXCEL to help with the matrix

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Unformatted text preview: manipulations, but make sure you understand what is going on. Check your work if you wish using MINITAB or other statistics software. a) 1 ) (-X X t . b) ) ( X X adj t . e) The leverages. d) 3 3 2 2 1 1 ˆ x b x b x b b y + + + = e) The OLS line equation if the graph is forced through the origin. 3. If y is regressed on x1, x2, and x3 and H is the hat matrix, find: a) The entries of Y-HY. b) The sum of the squares of the residuals (i.e. SSE). Hint: It is pretty easy to find the residuals! c) The coefficient of determination, namely R 2 ....
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ECON 337 Assignment 1 Fall 2007 - manipulations but make...

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